What Does it Take to Call a Strike? Three Biases in Umpire Decision Making

Do Major League Baseball umpires call balls and strikes solely in response to pitch location? No. Analyzing over one million pitches, we find that the strike zone contracts in 2-strike counts and expands in 3-ball counts, and that umpires are reluctant to call two strikes in a row. Effect sizes can be dramatic: for the average umpire, the probability of a called strike in 2-strike counts drops by as much as 19 percentage points in the corners of the strike zone; for some umpires, the chance of a called strike drops from a coin flip to almost zero. We structurally estimate each umpire’s aversions to miscalling balls and strikes in different game states. If an umpire is unbiased, he would only need to be 50% sure that a pitch is a strike in order to call a strike half the time. In fact, the average umpire needs to be 64% sure of a strike in order to call strike three half the time. Moreover, the least biased umpire still needs to be 55% sure of a strike in order to call strike three half the time. In other words, every umpire is biased. Because the biases are strongest at the top and bottom of the strike zone, pitchers should shift their pitches towards the top or bottom in 3-ball counts and towards the left or right in 2-strike counts.